Abstract
This research article expands the formal representation of human thinking to a most generalized hybrid theory, namely, complex
q
-rung orthopair fuzzy
N
-soft set. It is able to capture a great deal of graded imprecision and vagueness, which so often appear together in human interpretations. This model renders a parameterized mathematical tool for the ranking-based fuzzy modeling of two-dimensional paradoxical data. To that purpose, the proposed theory integrates complex
q
-rung orthopair fuzzy sets with the parametric structure of
N
-soft sets. The framework that arises captures information beyond the confined space of complex intuitionistic fuzzy
N
-soft sets and complex Pythagorean fuzzy
N
-soft sets, with the assistance of a parameter
q
. We establish the basic set-theoretical operations of this model and prove some of its fundamental properties. The Einstein and other elementary algebraic operations on complex
q
-rung orthopair fuzzy
N
-soft values shall be introduced to broaden the mathematical toolbox of this field. Its relationships with contemporary approaches shall demonstrate its outstanding flexibility. Moreover, we establish two competent multicriteria decision-making algorithms that capture the nuances of periodical inconsistent data. Their feasibility shall be demonstrated with an explicit application to the selection of optimum aerospace technology required for the economic development of the Mexican space agency. A comparative analysis of both strategies with the prevailing techniques substantiates their rationality. In addition, we illustrate this comparative study with an explicative bar chart that shows the compatibility of their outcomes. Finally, we examine the functionality of the proposed model and compare it with alternative theories.